Adopting Pade Approximation for First Order plus Dead Time Models for Blending Process: An Advance Study

Abstract

Dead-time is a typical occurrence in real-time processes, and it happens when a process variable fails to respond to changes in the set point. The presence of dead time in systems makes it difficult to govern and stabilize them, particularly in control feedback loops. Padé approximation provides a predictable approximation of dead time in continuous process systems, which can be used in subsequent simulations of similar First Order plus Dead Time Models. The classic Padé approximation, on the other hand, presents a shock at time t=0 due to the same numerator-denomi-nator derivative power. This generates an erroneous estimate of the dead time. Increasing orders of Padé approximation are used to avoid this issue. The corresponding First Order plus Dead-Time models of two blending systems of orders four and seven are discussed in the following work. The accuracy of the response grows as the orders of the Padé approximation increase. Instead of having one massive drop in the negative zone (as seen in the first few orders of Padé approximation), the oscillations are amplified on a much smaller scale, and the approximation tries to synchronize with the intended response curve in the positive region. MATLAB is used for all simulations.